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1、第六讲 几何元素的相对位置Lesson 6:Relative Position of Geometric elements1 1 平行问题平行问题 Parallel(1)(1)直线与平面平行直线与平面平行 Line parallel to Plane定理：定理：若一直线平行于平面上的某一直线，则该直线若一直线平行于平面上的某一直线，则该直线与此平面必相互平行。与此平面必相互平行。A line is parallel to a plane if it is parallel to a line in the plane.PL1L2L1/L2 L1/P直线与平面平行直线与平面平行 PARALLEL
2、ISM:LINES AND PLANESAB CDEFab cdefn a c b m abcmn例例1：过：过M点作直线点作直线MN平行于平面平行于平面ABC。Ex1:Construct line MN through M,required MNABC有无数解有无数解Countless solutions正平线正平线A frontal line例例2：过：过M点作直线点作直线MN平行于平行于V面和平面面和平面ABC。Ex2:Construct line MN,required MNV plane and MNABCc b a m abcmn唯一解唯一解Exclusive solutionn
3、eebbafadfdkk例例3：判断直线：判断直线AB是否平行于是否平行于DEF.Ex3:Is the line AB parallel to DEF?PL2Al laa L1l2l2 l1 l1L例例4:过过A点作与直线点作与直线L平行的平面平行的平面PEx3:Construct plane P through point A,required P parallel to given line L例例5 5 过过A A点作平面点作平面P/LP/L，且要求，且要求P P为正垂面为正垂面。Ex4:Construct plane P through point A,required P/L and
4、 PVl la aAB/P 且且AB=45 求求ABEx5:Reqd:Complete projection of ABp pa ab b由于P的V投影积聚为直线，则a b 平行于P，从而作出a b 。PV,plane appears as a line on frontal plane,a b P2、平面与平面平行、平面与平面平行 Parallel planes 若一平面上的若一平面上的两相交直两相交直线线对应平行于另一平面上对应平行于另一平面上的的两相交直线两相交直线，则这两平，则这两平面相互平行。面相互平行。If a pair of intersecting lines in one p
5、lane is parallel to a pair of intersecting lines in a second plane,the planes are parallel.若两若两投影面垂直面投影面垂直面相互相互平行，则它们平行，则它们具有积聚性具有积聚性的的那组投影必相互平行。那组投影必相互平行。Two perpendicular planes are parallel if their collecting projections are parallel.f h abcdefha b c d e c f b d e a abcdefABCD EFGJabcd efgjPL1Ap
6、 p p pa aa a L2l1l1 l2 l2Q例例7 7：过：过A A点作与平面点作与平面P P平行的平面平行的平面Q QEx6:Construct Plane Q,required through point A and parallel to plane P例9：过A作Q/P。Construct Plane Q,required through point A and parallel to plane PPHa ap QHq acebbaddfcfekhkhOXmm例10：判断平面ABDC与平面EFHM是否平行,已知ABCDEFMHEx10:ABCDEFMH,determine w
7、hether or not the two planes ABDC and EFHM are parallel to each other.由于ek不平行于ac,故两平面不平行。pcqpabacbpa1b1c1a1b1c1例11：判断P、Q平面是否平行。Ex1：Determine whether or not the two planes P and Q are parallel to each other.考虑简化作图过程Thinking about simplifying the drawing.作业：作业：P21（3除外）除外）复习：教材复习：教材P143P145 Homework:P21（except for 3）Reference：Textbook P143P145
画法几何课件：第六讲 几何元素的相对位置 (2)
